Search Images Maps Play YouTube News Gmail Drive More »
Sign in
 Books Books
If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
The first six books of the Elements of Euclid, with numerous exercises - Page 13
by Euclides - 1853 - 147 pages
Full view - About this book

The Foundations of Geometry and the Non-Euclidean Plane

G.E. Martin - Mathematics - 1997 - 536 pages
...the vertical angles equal to one another. (Theorem 14.11) 16. In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. (Theorem 17.9) 17. In any triangle two angles taken together in any manner are...
Limited preview - About this book

Geometry: A Comprehensive Course

Daniel Pedoe - Mathematics - 1988 - 468 pages
...another, they make the vertical angles equal to one another. 16 In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. 17 In any triangle two angles taken together in any manner are less than two right...
Limited preview - About this book

The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - Geometry, Non-Euclidean - 1993 - 320 pages
...students' memory, Euclid's proof is summarized below. Proposition 16. In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. PROOF: Let ABC be a triangle, and let one side of it BC be produced to D (Fig....
Limited preview - About this book

The Irish Law Times and Solicitors' Journal, Volume 37

Law - 1903 - 960 pages
...numbers is 13, the difference of their squares is 39. Find the numbers. SECOND PAPEK. EUCLID. 2. I f any side of a triangle be produced, the exterior angle is greater than either of the interior non-adjacent angles. 1. Prove that, it at a point in a right liiic, two other right lines on opposite...
Full view - About this book

Steno on Muscles: Introduction, Texts, Translations

Troels Kardel - Medical - 1994 - 270 pages
...respectively, namely those which the equal sides subtend. I. 16. In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. I. 18. In any triangle the greater side subtends the greater angle. I. 20. In...
Full view - About this book

The Scientific Letters and Papers of James Clerk Maxwell: Volume 1, 1846-1862

James Clerk Maxwell - Science - 1990 - 836 pages
...and annotations on the flyleaf by Maxwell, is in Maxwell's library (Cavendish Laboratory, Cambridge). (Theorem) ' If one side of a triangle be produced,...exterior angle is greater than either of the interior, and opposite angles' (Elements: 20). the angle ADB (Prop. 5). Upon AB describe a segment of a circle...
Limited preview - About this book

Tradition, Transmission, Transformation: Proceedings of Two Conferences on ...

F. Jamil Ragep, Sally P. Ragep, Steven John Livesey - Science - 1996 - 634 pages
...the three propositions quoted by Thabit b. Qurra. Theorem I,16: In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles.35 Table I 36 35 Heath [1956], vol. l,p. 279. 36 Since Thabit omitted here the...
Limited preview - About this book

Foundations and Fundamental Concepts of Mathematics

Howard Whitley Eves - Mathematics - 1997 - 370 pages
...line. Let us briefly consider, for example, Proposition I 16: In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. A precis of Euclid's proof runs as follows. Let ABC (Figure 2.2) be the given...
Limited preview - About this book

A Course in Modern Geometries

Judith Cederberg - Mathematics - 2004 - 472 pages
...another, they make the vertical angles equal to one another. 16. In any triangle if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. 17. In any triangle two angles taken together in any manner are less than two...
Limited preview - About this book

The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Mathematical Association of America - Mathematics - 2003 - 572 pages
...they make the vertical angles equal to one another. Prop. 16: In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. Prop. 19: In any triangle the greater angle is subtended by the greater side....
Limited preview - About this book